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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font> is  <a href="collsp.html#V3" title="COLLSP:attr.3">transitive</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="anproj_2.html#D8" target="_self" title="ANPROJ_2:def.8">ANPROJ_2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">q</font>, <font color="Olive" title="b2">r</font>, <font color="Olive" title="b3">r1</font>, <font color="Olive" title="b4">r2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>  st <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">q</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">q</font>,<font color="Olive" title="b3">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">q</font>,<font color="Olive" title="b4">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b2">r</font>,<font color="Olive" title="b3">r1</font>,<font color="Olive" title="b4">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font>, <font color="Maroon" title="c5">r1</font>, <font color="Maroon" title="c6">r2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="anproj_1.html#K5" title="ANPROJ_1:func.5">ProjectiveSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c6">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E63">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E64">A2</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E65">A3</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">r1</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E4:67"/><span class="lab"><font color="Green" title="E66">A4</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c6">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">u1</font>, <font color="Maroon" title="c8">v1</font>, <font color="Maroon" title="c9">w1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E6:67"/><span class="lab"><font color="Green" title="E67">A5</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c7">u1</font>
 <span class="kw">and </span><br/><a NAME="E7:67"/><span class="lab"><font color="Green" title="E68">A6</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c8">v1</font>
 <span class="kw">and </span><br/><a NAME="E8:67"/><span class="lab"><font color="Green" title="E69">A7</font></span>: 
<font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c9">w1</font>
 <span class="kw">and </span><br/><a NAME="E9:67"/><span class="lab"><font color="Green" title="E70">A8</font></span>: 
not <font color="Maroon" title="c7">u1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E10:67"/><span class="lab"><font color="Green" title="E71">A9</font></span>: 
not <font color="Maroon" title="c8">v1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E11:67"/><span class="lab"><font color="Green" title="E72">A10</font></span>: 
not <font color="Maroon" title="c9">w1</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E12:67"/><span class="lab"><font color="Green" title="E73">A11</font></span>: 
<font color="Maroon" title="c7">u1</font>,<font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c9">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E64">A2</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E14:67"/><span class="lab"><font color="Green" title="E74">A12</font></span>: 
not <font color="Maroon" title="c10">v</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E15:67"/><span class="lab"><font color="Green" title="E75">A13</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c10">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T42" title="ANPROJ_1:th.42">ANPROJ_1:42</a></span>;<br/>
<a NAME="E16:67"/><span class="lab"><font color="Green" title="E76">A14</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c8">v1</font>,<font color="Maroon" title="c10">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E74">A12</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E75">A13</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E68">A6</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E71">A9</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">u3</font>, <font color="Maroon" title="c12">v3</font>, <font color="Maroon" title="c13">w3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E18:67"/><span class="lab"><font color="Green" title="E77">A15</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c11">u3</font>
 <span class="kw">and </span><br/><a NAME="E19:67"/><span class="lab"><font color="Green" title="E78">A16</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c12">v3</font>
 <span class="kw">and </span><br/><a NAME="E20:67"/><span class="lab"><font color="Green" title="E79">A17</font></span>: 
<font color="Maroon" title="c6">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c13">w3</font>
 <span class="kw">and </span><br/><a NAME="E21:67"/><span class="lab"><font color="Green" title="E80">A18</font></span>: 
not <font color="Maroon" title="c11">u3</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E22:67"/><span class="lab"><font color="Green" title="E81">A19</font></span>: 
not <font color="Maroon" title="c12">v3</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E23:67"/><span class="lab"><font color="Green" title="E82">A20</font></span>: 
not <font color="Maroon" title="c13">w3</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E24:67"/><span class="lab"><font color="Green" title="E83">A21</font></span>: 
<font color="Maroon" title="c11">u3</font>,<font color="Maroon" title="c12">v3</font>,<font color="Maroon" title="c13">w3</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E66">A4</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E25:67"/><span class="lab"><font color="Green" title="E84">A22</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c12">v3</font>,<font color="Maroon" title="c10">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E74">A12</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E75">A13</font></span></a>, <a class="txt" href="#E19:67"><span class="lab"><font color="Green" title="E78">A16</font></span></a>, <a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E81">A19</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">u2</font>, <font color="Maroon" title="c15">v2</font>, <font color="Maroon" title="c16">w2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E27:67"/><span class="lab"><font color="Green" title="E85">A23</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c14">u2</font>
 <span class="kw">and </span><br/><a NAME="E28:67"/><span class="lab"><font color="Green" title="E86">A24</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c15">v2</font>
 <span class="kw">and </span><br/><a NAME="E29:67"/><span class="lab"><font color="Green" title="E87">A25</font></span>: 
<font color="Maroon" title="c5">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c16">w2</font>
 <span class="kw">and </span><br/><a NAME="E30:67"/><span class="lab"><font color="Green" title="E88">A26</font></span>: 
not <font color="Maroon" title="c14">u2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E31:67"/><span class="lab"><font color="Green" title="E89">A27</font></span>: 
not <font color="Maroon" title="c15">v2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E32:67"/><span class="lab"><font color="Green" title="E90">A28</font></span>: 
not <font color="Maroon" title="c16">w2</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E33:67"/><span class="lab"><font color="Green" title="E91">A29</font></span>: 
<font color="Maroon" title="c14">u2</font>,<font color="Maroon" title="c15">v2</font>,<font color="Maroon" title="c16">w2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>;<br/>
<a NAME="E34:67"/><span class="lab"><font color="Green" title="E92">A30</font></span>: 
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c15">v2</font>,<font color="Maroon" title="c10">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E74">A12</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E75">A13</font></span></a>, <a class="txt" href="#E28:67"><span class="lab"><font color="Green" title="E86">A24</font></span></a>, <a class="txt" href="#E31:67"><span class="lab"><font color="Green" title="E89">A27</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c17">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E36:67"/><span class="lab"><font color="Green" title="E93">A31</font></span>: 
not <font color="Maroon" title="c17">u</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">and </span><br/><a NAME="E37:67"/><span class="lab"><font color="Green" title="E94">A32</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="anproj_1.html#K2" title="ANPROJ_1:func.2">Dir</a> <font color="Maroon" title="c17">u</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_1.html#T42" title="ANPROJ_1:th.42">ANPROJ_1:42</a></span>;<br/>
<a NAME="E38:67"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c7">u1</font>,<font color="Maroon" title="c17">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E93">A31</font></span></a>, <a class="txt" href="#E37:67"><span class="lab"><font color="Green" title="E94">A32</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E67">A5</font></span></a>, <a class="txt" href="#E9:67"><span class="lab"><font color="Green" title="E70">A8</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E39:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A33</font></span>: 
<font color="Maroon" title="c17">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c9">w1</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E73">A11</font></span></a>, <a class="txt" href="#E16:67"><span class="lab"><font color="Green" title="E76">A14</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E40:67"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c11">u3</font>,<font color="Maroon" title="c17">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E93">A31</font></span></a>, <a class="txt" href="#E37:67"><span class="lab"><font color="Green" title="E94">A32</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E77">A15</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E80">A18</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E41:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A34</font></span>: 
<font color="Maroon" title="c17">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c13">w3</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:67"><span class="lab"><font color="Green" title="E83">A21</font></span></a>, <a class="txt" href="#E25:67"><span class="lab"><font color="Green" title="E84">A22</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E42:67"/>
 <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c14">u2</font>,<font color="Maroon" title="c17">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E93">A31</font></span></a>, <a class="txt" href="#E37:67"><span class="lab"><font color="Green" title="E94">A32</font></span></a>, <a class="txt" href="#E27:67"><span class="lab"><font color="Green" title="E85">A23</font></span></a>, <a class="txt" href="#E30:67"><span class="lab"><font color="Green" title="E88">A26</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E43:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A35</font></span>: 
<font color="Maroon" title="c17">u</font>,<font color="Maroon" title="c10">v</font>,<font color="Maroon" title="c16">w2</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:67"><span class="lab"><font color="Green" title="E91">A29</font></span></a>, <a class="txt" href="#E34:67"><span class="lab"><font color="Green" title="E92">A30</font></span></a>, <a class="ref" href="anproj_1.html#T9" title="ANPROJ_1:th.9">ANPROJ_1:9</a></span>;<br/>
<a NAME="E44:67"/>
not  <a href="anproj_1.html#R1" title="ANPROJ_1:pred.1">are_Prop</a> <font color="Maroon" title="c17">u</font>,<font color="Maroon" title="c10">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E63">A1</font></span></a>, <a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E93">A31</font></span></a>, <a class="txt" href="#E37:67"><span class="lab"><font color="Green" title="E94">A32</font></span></a>, <a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E74">A12</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E75">A13</font></span></a>, <a class="ref" href="anproj_1.html#T35" title="ANPROJ_1:th.35">ANPROJ_1:35</a></span>;<br/>
<a NAME="E45:67"/><span class="kw">then </span>
<font color="Maroon" title="c9">w1</font>,<font color="Maroon" title="c16">w2</font>,<font color="Maroon" title="c13">w3</font> <a href="anproj_1.html#R2" title="ANPROJ_1:pred.2">are_LinDep</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E93">A31</font></span></a>, <a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E74">A12</font></span></a>, <a class="txt" href="#E39:67"><span class="lab"><font color="Green" title="E95">A33</font></span></a>, <a class="txt" href="#E43:67"><span class="lab"><font color="Green" title="E97">A35</font></span></a>, <a class="txt" href="#E41:67"><span class="lab"><font color="Green" title="E96">A34</font></span></a>, <a class="ref" href="anproj_1.html#T19" title="ANPROJ_1:th.19">ANPROJ_1:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E46:67"/>
<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">r1</font>,<font color="Maroon" title="c6">r2</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E69">A7</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E72">A10</font></span></a>, <a class="txt" href="#E29:67"><span class="lab"><font color="Green" title="E87">A25</font></span></a>, <a class="txt" href="#E32:67"><span class="lab"><font color="Green" title="E90">A28</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E79">A17</font></span></a>, <a class="txt" href="#E23:67"><span class="lab"><font color="Green" title="E82">A20</font></span></a>, <a class="ref" href="anproj_2.html#T24" target="_self" title="ANPROJ_2:th.24">Th24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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